Efficient Marginalization-Based MCMC Methods for Hierarchical Bayesian Inverse Problems

DOI10.1137/18M1220625WikidataQ127254508 ScholiaQ127254508MaRDI QIDQ5237188

Arvind K. Saibaba, Johnathan M. Bardsley, D. Andrew Brown, Alen Alexanderian

Publication date: 17 October 2019

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.01091

zbMATH Keywords

inverse problemsMarkov chain Monte Carlolow-rank approximationshierarchical Bayesian approachone-block algorithm

Mathematics Subject Classification ID

Related Items (3)

Randomized approaches to accelerate MCMC algorithms for Bayesian inverse problems ⋮ Optimization-Based Markov Chain Monte Carlo Methods for Nonlinear Hierarchical Statistical Inverse Problems ⋮ Optimal experimental design for infinite-dimensional Bayesian inverse problems governed by PDEs: a review

Uses Software

• GMRFLib
• BayesDA

Cites Work

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• Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
• The pseudo-marginal approach for efficient Monte Carlo computations
• Scalable and efficient algorithms for the propagation of uncertainty from data through inference to prediction for large-scale problems, with application to flow of the antarctic ice sheet
• Statistical and computational inverse problems.
• Markov chains for exploring posterior distributions. (With discussion)
• An exploration of aspects of Bayesian multiple testing
• Dimension-independent likelihood-informed MCMC
• Efficient MCMC-based image deblurring with Neumann boundary conditions
• An introduction to infinite-dimensional analysis
• Inverse problems: A Bayesian perspective
• MCMC-Based Image Reconstruction with Uncertainty Quantification
• A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion
• An efficient approach for computing optimal low-rank regularized inverse matrices
• Analysis of the Gibbs Sampler for Hierarchical Inverse Problems
• Fast Algorithms for Bayesian Uncertainty Quantification in Large-Scale Linear Inverse Problems Based on Low-Rank Partial Hessian Approximations
• Transport Map Accelerated Markov Chain Monte Carlo
• Fast Sampling in a Linear-Gaussian Inverse Problem
• Optimal Low-rank Approximations of Bayesian Linear Inverse Problems
• Sampling-Based Approaches to Calculating Marginal Densities
• Hypermodels in the Bayesian imaging framework
• Handbook of Markov Chain Monte Carlo
• Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
• Low-Rank Matrix Approximation Using the Lanczos Bidiagonalization Process with Applications
• Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography
• Efficient Gaussian Sampling for Solving Large-Scale Inverse Problems Using MCMC
• Point Spread Function Estimation in X-Ray Imaging with Partially Collapsed Gibbs Sampling
• Gaussian Markov Random Fields
• Low-Rank Independence Samplers in Hierarchical Bayesian Inverse Problems
• Equation of State Calculations by Fast Computing Machines
• A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems Part I: The Linearized Case, with Application to Global Seismic Inversion
• Introduction to Bayesian Scientific Computing
• Monte Carlo sampling methods using Markov chains and their applications
• Priorconditioners for linear systems
• An adaptive Metropolis algorithm
• Prior distributions for variance parameters in hierarchical models (Comment on article by Browne and Draper)

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